Abstract
Based on the velocity relationship between two points on the mobile platform, the new expression to construct the forward Jacobian matrix of parallel mechanism by its branched chains is deduced. This method is able to be used for the automatic generation of Jacobian matrix of parallel mechanism or hybrid mechanism, the correctness of presented method is validated by analyzing the planar 5R parallel mechanism. The multiply operations in the new expression are (36fp+6fa) times less than that in the Jacobian matrix deduced by Monsarrat and Gosselin in literature five while the flexible linkages are omitted by comparing two expressions.
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References
Orin, D.E., Schrader, W.W.: Efficient Jacobian determination for robot manipulators. In: Proceedings of the Sixth World Congress on the Theory of Machines and Mechanisms, New Delhi, India, vol. II, pp. 994–997 (1984)
Al-Gallaf, E.A.: Neurofuzzy inverse Jacobian mapping for multi-finger robot hand control. Journal of Intelligent and Robotic Systems: Theory and Applications 39, 17–42 (2004)
Murry, R.M., Li, Z.X., Sastry, S.S.: A mathematical introduction to robotic manipulation. China Machine Press, Beijing (1998) (in Chinese)
Ye, P., Sun, H.X., Tan, Y., et al.: A modified method for Jacobian matrix with screw theory and vector product. Mechanical Science and Technology 24, 353–356 (2005) (in Chinese)
Fenton, R.G., Xi, F.: Determination of the robot Jacobian using the algebra of rotations. American Society of Mechanical Engineers 25, 75–81 (1990)
Xiong, Y.L., Yin, Z.P., Xiong, C.H.: Robotic manipulation. Hubei Science and Technology Press, Wuhan (2002) (in Chinese)
Huang, Z., Kong, L.F., Fang, Y.F.: Theory of parallel robots’ mechanism and control. China Machine Press, Beijing (1997) (in Chinese)
Angeles, J.: Fundamentals of robotic mechanical systems: theory, methods, and algorithms. China Machine Press, Beijing (2004) (in Chinese)
Yu, H.: Study on the mechanism and kinematics of 6-HTRT parallel robot. Doctorial dissertation, Harbing Institute of Technology 4, 47–48 (2002) (in Chinese)
Monsarrat, B., Gosselin, C.M.: Jacobian matrix of general parallel and hybrid mechanisms with rigid and flexible links: a software-oriented approach. In: Proceedings of the ASME Design Engineering Technical Conference, 27th Biennial Mechanisms and Robotics Conference, Montreal, Que, pp. 461–470 (2002)
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© 2008 Springer-Verlag Berlin Heidelberg
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Xin, H., Huang, Q., Duan, X., Yu, Y. (2008). A New Expression to Construct Jacobian Matrix of Parallel Mechanism. In: Xiong, C., Huang, Y., Xiong, Y., Liu, H. (eds) Intelligent Robotics and Applications. ICIRA 2008. Lecture Notes in Computer Science(), vol 5314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88513-9_13
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DOI: https://doi.org/10.1007/978-3-540-88513-9_13
Publisher Name: Springer, Berlin, Heidelberg
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